To people familiar with Deltarune's save files: does the game record how many turns you took to beat Gerson?

I'm currently trying to beat Gerson, so that I can finish Chapter 4 before 5 comes out. But the last few turns (from 17 onwards -- go figure) have proven to be a very difficult wall to climb. So I would like to ask, does the game actually record how many turns the fight took? Or does it ultimately treat everything the same regardless of if I took 15 or 20 turns?

Yes, I know there is some dialogue that gets skipped if I complete the fight more quickly, but I mean in the long run. If the game records the number of turns in the savefile, then I worry by not taking the full number of turns I might miss out on extra content in future chapters, since what he says towards the end of the fight sounds pretty darn important.